Class 11 Notes Physics Vectors And Equilibrium Numerical Problems – Concept Questions KPK G11 Physics Chapter 2 Q.1) Is it possible to add three vectors of equal magnitude but different directions to get the zero vector? Illustrate with a diagram.
Yes, if three vectors form an equilateral triangle, the result will be the zero vector, because in this case the sum of the two vectors will be equal in magnitude but in the opposite direction to the third vector.
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It can be seen in the figure that the result of AandBi.e.Ris is equal but in the opposite direction to Ci.e.R = – C. Thus,
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Q.2) The magnitude of three vectors is 2 m, 3 m and 5 m, respectively. Instructions are available. Can these vectors be added to produce zero? Illustrate with a diagram.
For it to be zero, the resultant of two vectors must be equal in magnitude but in the opposite direction to the third vector. Thus, if the magnitudes of vectors A and Bare are added, their resultant magnitude “R” is given as;
Which is approximately equal to the third vector. To produce zero, the direction of R must be opposite to the direction of Ci.e.R, must be -Cas shown in the figure;
The unit vectors, ĵ, and k̂ represent the x, y, z directions of the vectors, that is, the direction of the vectors in the Cartesian plane and are defined as follows;
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For example, if a force Fis is applied to an object in the x direction, its unit vector î is given as;
The dot product of two vectors is defined as the product of the magnitude of one vector and the component of the other vector in the direction of the first vector.
Since cosθ is negative between 90° and 270°, so the dot product can be negative for these values of θ.
Q.5) A and B are two non-zero vectors. How can its scalar product be equal to zero? And how can its vector product be zero?
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The vector product of two vectors is defined as the product of the magnitude of one vector and the component of another vector perpendicular to the first vector.
If two vectors are parallel or antiparallel to each other, the angle between them is θ = 0° or 180°. As sin0° = sin 180° = 0
Q. 6) Suppose you are given an unknown vector A. The dot product of A with the unknown vector B is zero. Similarly, the vector product of A with B is zero. What can you conclude about B?
A body is said to be in perfect equilibrium if the sum of all the forces and moments acting on it does not change its transverse motion and rotation. that is, the net force and net torque acting on it must be zero.
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Thus, if only one force acts on the particle, the condition of net force and zero net torque cannot be satisfied. Therefore, the particle cannot be in equilibrium.
Q.8) To open a door with the handle on the right side and the hinges on the left side, a torque must be applied. Is the torque clockwise or counterclockwise when viewed from above? Does your answer depend on whether the door opens towards you or away from you?
If the door opens towards us, we have to pull the door handle, meaning the direction of the force is towards us. Thus, if we align the fingers of our right hand along “r” (the distance between the hinges and the line of action of the force) and twist them in the direction of “F”, our thumb will point in the downward direction, ie clockwise torque. produced
If the door opens away from us, we have to push the door handle, which means the direction of the force is away from us. So if we line up the fingers of our right hand along the “r” and twist them in the direction of the “F”, our finger will point up, which means that a counterclockwise torque will be generated.
Solution: 11th Class Physics Chapter 2 Vectors And Equilibrium Notes
For a large key, the distance between the line of action of the force and the axis of rotation will be large. Therefore, even a small amount of force can produce a large amount of torque that can cause the screw to break.
Q.10) Centripetal force is a force that is always directed towards a point. Can the centripetal force produce a torque at this point?
No, the centripetal force cannot produce a torque because the line of action of the force passes through the axis of rotation, i.e. the angle between r and Fis is 0°. Therefore, the torque is zero
2. Now place them head to tail, putting the tail of the second vector to the head of the first vector according to the selected table in the given direction.
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3. Then connect the tail of the first vector to the head of the last, which gives another vector that is the sum of these vectors, called the resultant vector.
To add these vectors we redraw them to a common scale and place them head to tail as mentioned above. Therefore, the tail of vector B is at the head of vector A. Several tails of A with heads of B give another vector that is the sum of these vectors, called the resultant vector R, as shown in the figure below. The result will have the same effect as the combined effect of both vectors.
These can be added head to tail as before; that is, arrange them head to tail so that the tail of each vector is at the head of the previous vector. Then draw the resulting vector by connecting the tail of the first vector to the head of the last. how;
Subtracting one vector from another means adding the negative of the vector to the first.
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If vector A is subtracted from vector A, first find the negative of vector B (which is –B). Then follow the rules of adding vectors to get the result shown in the figure;
Q.2) If a vector is multiplied by a positive scalar, how is the result related to the original vector? What if the scalar is zero? negative?
If the vector A is multiplied by a positive scalar ‘n’, the length of the vector becomes n times the length of the vector A. While the direction of the vector remains unchanged. that is to say
When this vector ‘A’ is multiplied by a scalar n= 2, the length of the vector is doubled and the direction remains the same as shown in figure 2;
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If the vector A is multiplied by a negative scalar ‘-n’, the length of the vector is equal to n times the length of the vector A. While the direction of the vector is reversed. that is to say
When the vector shown in Figure 1 is multiplied by the scalar n = – 2, the length of the vector is doubled and the direction is reversed.
If a vector is divided or resolved into two or more components perpendicular to each other, such components are called orthogonal components of this vector.
î + Ayĵ ……………… (i)
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From figure 1 consider the triangle OPQ without considering the sides as vectors as shown in figure 2. This forms the right triangle OPQ which we have for.
Equation (ii) and equation (iii) are used to express the components in terms of their vector. Substituting equation (ii) and equation (iii) into equation (i), we get
A= A cosθî+ A sinθĵ …………….. (iv)
) …………….. (v)
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The magnitude of the vector can now be determined from equation (v) if the magnitude values of the components are known.
Addition of Vectors by Rectangular Components: The basic rule of adding vectors by definition is the head-to-tail rule. But sometimes it becomes difficult to draw vectors according to the head-to-tail rule. Another method for adding vectors is called the analytic method, also known as the rectangular component method. “The rectangular components of a vector are the effective values of the vector in all three directions.”
The state of a body that does not change under the influence of various forces and moments acting together in translational and rotational motion is called equilibrium.
When a body is at rest under the influence of several forces acting together, the body is said to be in static equilibrium.
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For example, a book on a table is in static equilibrium; the weight “mg” of the book is equal to the normal reaction force in the table.
When a body is moving at the same speed under the influence of several combined forces, the body is said to be in dynamic equilibrium.
When a body moves with uniform linear velocity, the body is said to be in dynamic translational equilibrium.
When a body moves with the same angular velocity, the body
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